Some eyebrows were raised in October when producers cast the sandy-haired, relatively unknown Craig in the next James Bond film, "Casino Royale."
But Connery, 75, told British Broadcasting Corp. television that he approved.
"Craig's a great choice, really interesting, different," Connery said in comments released Friday by the broadcaster. The full interview is due to air Monday.
"He's a good actor. It's a completely new departure," he added.
The respect is mutual. Craig told a news conference in October that Connery was his favorite 007.
Connery was the first actor to play Bond, appearing in six official Bond films beginning with "Dr. No" in 1962 and ending in 1971 with "Diamonds Are Forever."
Roger Moore, George Lazenby, Timothy Dalton and Pierce Brosnan have also starred as the womanizing, gadget-loving spy.
Connery said he'd left the role in part "because I got really fed up with the space stuff and special effects. I just found it getting more and more influential in the movies."
"Casino Royale" is due in theaters next November.
Craig is theand only the second Englishman to star as Agent 007 in the movie series. (Moore played Bond in seven films from 1973-85.)
Relatively unknown outside Britain, Craig appeared in the landmark 1990s British TV drama "Our Friends in the North" and in films including "The Mother," "Enduring Love" and "Layer Cake."
He played Paul Newman's sinister son in "Road to Perdition," was poet Ted Hughes opposite Gwyneth Paltrow's Sylvia Plath in "Sylvia" and starred in this year's thriller "The Jacket" with Adrien Brody.